Solve a - b: Subtracting a Positive Number from a Negative Number

Integer Subtraction with Mixed Signs

a is a negative number.

b is a positive number.

Therefore, a - b is....?

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Step-by-step written solution

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1

Understand the problem

a is a negative number.

b is a positive number.

Therefore, a - b is....?

2

Step-by-step solution

We test using an example:

We define that

a = -1

b = 2

Now we replace in the exercise:

-1-(2) = -1-2 = -3

In this case, the result is negative!

 

We test a case where the value of b is less than a

We define that

a = -2

b = 1

 

-2-(1) = -2-1 = -3

 

In this case, the result is again negative.

Since it is not possible to produce a case where a is greater than b (because a negative number is always less than a positive number),

The result will always be the same: "negative", and that's the solution!

3

Final Answer

Negative

Key Points to Remember

Essential concepts to master this topic
  • Rule: Subtracting positive from negative always produces negative result
  • Technique: Transform a - b to a + (-b): -2 - 3 = -2 + (-3) = -5
  • Check: Use number line or test examples: -1 - 2 = -3 ✓

Common Mistakes

Avoid these frequent errors
  • Thinking the result could be positive
    Don't assume that subtracting might make the number "less negative" = positive result! Since we're subtracting a positive number, we move further left on the number line, making the result more negative. Always remember: negative minus positive equals more negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why is the answer always negative when a negative minus a positive?

+

Think of it on a number line! Starting at a negative position and subtracting (moving left) a positive amount takes you further into negative territory. You can never reach zero or positive numbers this way.

What if the positive number b is really small?

+

Even if b = 0.001, subtracting it from any negative number still gives a negative result! For example: -5 - 0.001 = -5.001. The size doesn't matter - the direction does.

How is this different from a + b when both are negative?

+

That's addition of two negatives, which also gives negative. But here we have subtraction: a - b = a + (-b). So -2 - 3 becomes -2 + (-3) = -5.

Can I use concrete examples to understand this better?

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Absolutely! Think of temperature: if it's -5°C and drops by 3 more degrees, you get -8°C. Or money: owing 5andthenowing5 and then owing 3 more means you owe $8 total.

What's the fastest way to solve these problems?

+

Remember the pattern: negative - positive = more negative. You can also rewrite as addition: a - b = a + (-b), then add the absolute values and keep the negative sign.

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